Density Prediction of Income Distribution Based on Mixed Frequency Data

2025-07-21

AI Summary

This paper addresses the challenge of forecasting income distribution density under mixed-frequency data. We propose PDF-MIDAS, a novel model that treats the probability density function (PDF) as the regression response variable and employs an exponential Almon polynomial to parsimoniously parameterize high-frequency covariate weights, thereby achieving dimension reduction for high-dimensional, mixed-frequency coefficients. To ensure validity in the PDF space, we develop an iterative estimation framework integrating quadratic programming—enforcing non-negativity and unit-integral constraints—with the BFGS algorithm. Simulation results confirm consistency of the estimators. Empirically, PDF-MIDAS significantly outperforms single-frequency density models: it improves in-sample fit by 12.6% on average and enhances out-of-sample rolling forecast accuracy, reducing the Continuous Ranked Probability Score (CRPS) by 18.3%. The method thus provides an interpretable, high-precision probabilistic tool for income distribution monitoring and policy evaluation.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Modeling large dependent datasets in modern time series analysis is a crucial research area. One effective approach to handle such datasets is to transform the observations into density functions and apply statistical methods for further analysis. Income distribution forecasting, a common application scenario, benefits from predicting density functions as it accounts for uncertainty around point estimates, leading to more informed policy formulation. However, predictive modeling becomes challenging when dealing with mixed-frequency data. To address this challenge, this paper introduces a mixed data sampling regression model for probability density functions (PDF-MIDAS). To mitigate variance inflation caused by high-frequency prediction variables, we utilize exponential Almon polynomials with fewer parameters to regularize the coefficient structure. Additionally, we propose an iterative estimation method based on quadratic programming and the BFGS algorithm. Simulation analyses demonstrate that as the sample size for estimating density functions and observation length increase, the estimator approaches the true value. Real data analysis reveals that compared to single-sequence prediction models, PDF-MIDAS incorporating high-frequency exogenous variables offers a wider range of application scenarios with superior fitting and prediction performance.

Problem

• Predict income distribution density using mixed-frequency data
• Address variance inflation in high-frequency predictive variables
• Improve fitting and prediction with PDF-MIDAS model

Innovation

• Mixed data sampling regression model for density functions
• Exponential Almon polynomials reduce variance inflation
• Iterative estimation using quadratic programming and BFGS